Two waves on identical strings have frequencies in a ratio of 2 to 1. If their wave speeds are the same, then how do their wavelengths compare?

Answer: λ1=λ2/2 (ν1 = 2*ν2)

Explanation: In order to explain this problem we have to use following expression for waves.

v=λ*ν; v is the wave speed. λ and ν are the wavelength and frequency of the wave, respectively.

we have two waves where ν1 = 2*ν2 then as the speed is the same for both waves, we have,

λ1*ν1=λ2*ν2 with ν1 = 2*ν2 then

λ1=λ2*ν2/v1=λ2*ν2 / (2*ν2) = λ2/2

λ1=λ2/2